I agree with Stickboy. But I want to add that the book?s basis for the ?no? answer is correct, and your instructor?s basis for the ?no? answer is wrong. Let me illustrate the difference.
Recall that the GFCI device is at the wall, somewhat distant from the sink. Current will pass through the GFCI, head towards the hair dryer along one wire (call it the ?hot wire? for my purposes), and then it will find two paths to take. Some (most???) of the current will pass through the internal wires and heating elements and motor of the hair dryer, and make its way back to the GFCI on the other wire (call it the ?cold wire? for my purposes). Some of the current will be short circuited somewhere within the hair dryer, and pass from the hot wire directly to the cold wire. From there, it returns to the GFCI. Please note that the total current leaving the GFCI along the hot wire is the same as the total current returning to the GFCI along the cold wire. The fact that some current took different paths along the way means nothing; the totals are the same. That is why, as Stickboy pointed out, the GFCI does not trip.
That is also why your book?s answer is correct. There are no paths for current to flow from the GFCI but not back to the GFCI; so the GFCI sees a balanced current. However, if you put your hand in the water (not recommended), you create a new path. The fact that the cord cap has only two wires, and not a third ground wire, means nothing, so your instructor?s answer was wrong. Current will flow along the hot wire, through you, into the floor and into the dirt, to the ground rod, up the GEC to the service point. The GFCI will see a difference in current from its hot wire to its cold wire, and it will trip. You will get a shock, but not long enough to feel it, and certainly not long enough to do you any harm
